SOME SPACES THAT SATISFY THE ANDREWS-CURTIS CONJECTURE
By
Ponaki Das1 and Sainkupar Marwein Mawiong2*
1Department of Mathematics, North-Eastern Hill University, Shillong, Meghalaya, India-793022
2Department of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong, Meghalaya, India-793022
Email: ponaki.das20@gmail.com, *Correspondence: skupar@gmail.com
(Received: December 26, 2023; In format: February 21, 2024; Revised: July 02, 2024; Accepted; October 07, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54214
Abstract
The Andrews-Curtis conjecture, a long-standing problem in algebraic topology, has remained a subject of intense research for decades. In this paper, we introduce a novel reduction method that expands the boundaries of finite topological spaces satisfying the conjecture. Our method builds upon the foundational work in the field and offers a fresh perspective on tackling this challenging problem. Through the application of our innovative reduction technique, we demonstrate the discovery of a substantial number of previously unidentified finite topological spaces that satisfy the Andrews-Curtis conjecture. Additionally, we investigate how our reduction method works together with reduction methods previously introduced by Ximena [7]. This collaborative investigation not only validates the efficacy of our method but also reveals intriguing connections between different reduction techniques, shedding light on the underlying mathematical structures governing the conjecture.
2020 Mathematical Sciences Classification: 06A99, 18B35, 55P10, 55P15.
Keywords: Finite spaces, Posets, Homotopically trivial spaces, Andrews-Curtis conjecture